Group #20243516 — subgroups

Subgroups — #20243516

Order 6016.

248 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15688993	C₂	1	2	yes	maximal
2	#15688886	C₂	1	4	yes	maximal
3	C₂×C₄×C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊Dic₄₇	—	2	2	no	—
5	C₂×C₄⋊Dic₄₇	—	2	2	no	—
6	C₂×C₄⋊Dic₄₇	C₂²	1	4	yes	—
7	C₂²×C₈×C₄₇	C₂²	1	2	yes	—
8	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
9	C₄×C₈×C₄₇	C₄	1	4	yes	complemented
10	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
11	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
12	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
13	C₂²×Dic₄₇	—	2	4	no	—
14	C₂×C₈×C₄₇	—	2	4	no	—
15	C₂×C₈×C₄₇	C₂×C₄	1	4	yes	—
16	C₄²×C₄₇	C₂×C₄	1	2	yes	—
17	C₄²×C₄₇	Q₈	1	2	yes	—
18	C₄⋊Dic₄₇	—	2	8	no	—
19	C₄⋊Dic₄₇	—	4	4	no	—
20	C₄⋊Dic₄₇	—	4	4	no	—
21	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
22	C₂×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
23	C₂×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
24	C₂×C₄×C₄₇	D₈	1	2	yes	—
25	C₂×C₄×C₄₇	SD₁₆	1	4	yes	—
26	C₂×C₄×C₄₇	Q₁₆	1	2	yes	—
27	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
29	C₂×C₄×C₄₇	#41	1	4	yes	—
30	C₂×Dic₄₇	—	4	4	no	—
31	C₂×Dic₄₇	—	4	4	no	—
32	C₂×Dic₄₇	—	4	4	no	—
33	C₈×C₄₇	—	2	4	no	—
34	C₂²×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
35	C₂²×C₄₇	#124	1	2	yes	—
36	C₂²×C₄₇	C₂×D₈	1	1	yes	characteristic
37	C₂²×C₄₇	C₂×SD₁₆	1	2	yes	—
38	C₂²×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
39	C₄×C₄₇	#106	1	4	yes	—
40	C₄×C₄₇	#107	1	4	yes	—
41	C₄×C₄₇	#117	1	2	yes	—
42	C₄×C₄₇	#125	1	2	yes	—
43	Dic₄₇	—	8	4	no	—
44	#1834	—	47	1	no	maximal, Sylow
45	C₂×C₄₇	#382	1	1	yes	characteristic
46	C₂×C₄₇	C₂×#106	1	1	yes	characteristic
47	C₂×C₄₇	C₂×#107	1	1	yes	characteristic
48	C₂×C₄₇	#486	1	2	yes	—
49	C₂×C₄₇	#487	1	2	yes	—
50	C₂×C₄×C₈	D₄₇	1	1	yes	characteristic
51	#384	—	47	2	no	—
52	#340	—	47	4	no	—
53	C₄₇	#1834	1	1	yes	characteristic, complemented, Sylow
54	C₂²×C₈	C₂×D₄₇	1	2	yes	—
55	C₂×C₄⋊C₄	—	47	4	no	—
56	C₂×C₄⋊C₄	—	94	2	no	—
57	C₂×C₄⋊C₄	—	94	2	no	—
58	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
59	C₄×C₈	Dic₄₇	1	4	yes	complemented
60	C₂²×C₄	—	94	4	no	—
61	C₂²×C₄	D₁₈₈	1	1	yes	characteristic
62	C₂²×C₄	D₁₈₈	1	1	yes	characteristic
63	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
64	C₂×C₈	—	2	4	no	—
65	C₂×C₈	C₂×Dic₄₇	1	4	yes	—
66	C₄⋊C₄	—	94	8	no	—
67	C₄⋊C₄	—	188	4	no	—
68	C₄⋊C₄	—	188	4	no	—
69	C₄²	Dic₉₄	1	2	yes	—
70	C₄²	C₂×Dic₄₇	1	2	yes	—
71	C₂³	C₂×D₁₈₈	1	1	yes	characteristic
72	C₂×C₄	—	188	4	no	—
73	C₂×C₄	—	188	4	no	—
74	C₂×C₄	—	188	4	no	—
75	C₂×C₄	#10625325	1	4	yes	—
76	C₂×C₄	D₃₇₆	1	2	yes	—
77	C₂×C₄	Dic₁₈₈	1	2	yes	—
78	C₂×C₄	C₄⋊Dic₄₇	1	2	yes	—
79	C₂×C₄	C₄⋊Dic₄₇	1	2	yes	—
80	C₂×C₄	C₂×Dic₉₄	1	1	yes	characteristic
81	C₂×C₄	#10625350	1	4	yes	—
82	C₂×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
83	C₈	—	2	4	no	—
84	C₂²	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
85	C₂²	#13094012	1	2	yes	—
86	C₂²	C₂×D₃₇₆	1	1	yes	characteristic
87	C₂²	C₂×#10625325	1	2	yes	—
88	C₂²	C₂×Dic₁₈₈	1	1	yes	characteristic
89	C₄	—	376	4	no	—
90	C₄	#13093956	1	4	yes	—
91	C₄	#13093958	1	4	yes	—
92	C₄	#13093983	1	2	yes	—
93	C₄	#13094016	1	2	yes	—
94	C₂	#15688989	1	1	yes	characteristic
95	C₂	C₂×#13093956	1	1	yes	characteristic
96	C₂	C₂×#13093958	1	1	yes	characteristic
97	C₂	#15689470	1	2	yes	—
98	C₂	#15689474	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#15688993

C₂

yes

maximal

#15688886

C₂

yes

maximal

C₂×C₄×C₈×C₄₇

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂²×C₈×C₄₇

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

C₄×C₈×C₄₇

C₄

yes

complemented

C₂²×C₄×C₄₇

D₄

yes

characteristic

C₂²×C₄×C₄₇

D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂×C₄

yes

—

C₄²×C₄₇

C₂×C₄

yes

—

C₄²×C₄₇

Q₈

yes

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₂³×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₄⋊C₄

yes

—

C₂×C₄×C₄₇

C₄⋊C₄

yes

—

C₂×C₄×C₄₇

D₈

yes

—

C₂×C₄×C₄₇

SD₁₆

yes

—

C₂×C₄×C₄₇

Q₁₆

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₇

#41

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₈×C₄₇

—

C₂²×C₄₇

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₄₇

#124

yes

—

C₂²×C₄₇

C₂×D₈

yes

characteristic

C₂²×C₄₇

C₂×SD₁₆

yes

—

C₂²×C₄₇

C₂×Q₁₆

yes

characteristic

C₄×C₄₇

#106

yes

—

C₄×C₄₇

#107

yes

—

C₄×C₄₇

#117

yes

—

C₄×C₄₇

#125

yes

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

—

C₂×C₄₇

#487

yes

—

C₂×C₄×C₈

D₄₇

yes

characteristic

#384

—

#340

—

C₄₇

#1834

yes

characteristic, complemented, Sylow

C₂²×C₈

C₂×D₄₇

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₄₇

yes

characteristic

C₄×C₈

Dic₄₇

yes

complemented

C₂²×C₄

—

C₂²×C₄

D₁₈₈

yes

characteristic

C₂²×C₄

D₁₈₈

yes

characteristic

C₂²×C₄

C₂²×D₄₇

yes

characteristic

C₂×C₈

—

C₂×C₈

C₂×Dic₄₇

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

188

—

C₄⋊C₄

—

188

—

C₄²

Dic₉₄

yes

—

C₄²

C₂×Dic₄₇

yes

—

C₂³

C₂×D₁₈₈

yes

characteristic

C₂×C₄

—

188

—

C₂×C₄

—

188

—

C₂×C₄

—

188

—

C₂×C₄

#10625325

yes

—

C₂×C₄

D₃₇₆

yes

—

C₂×C₄

Dic₁₈₈

yes

—

C₂×C₄

C₄⋊Dic₄₇

yes

—

C₂×C₄

C₄⋊Dic₄₇

yes

—

C₂×C₄

C₂×Dic₉₄

yes

characteristic

C₂×C₄

#10625350

yes

—

C₂×C₄

C₂²×Dic₄₇

yes

characteristic

C₈

—

C₂²

C₂×C₄⋊Dic₄₇

yes

characteristic

C₂²

#13094012

yes

—

C₂²

C₂×D₃₇₆

yes

characteristic

C₂²

C₂×#10625325

yes

—

C₂²

C₂×Dic₁₈₈

yes

characteristic

C₄

—

376

—

C₄

#13093956

yes

—

C₄

#13093958

yes

—

C₄

#13093983

yes

—

C₄

#13094016

yes

—

C₂

yes

C₂

yes

C₂

yes

C₂

yes

—

C₂

#15689474

yes

—

	subgroup	G/H
center	C₂³	C₂×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₂×C₄×C₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂×D₄
hypercenter	C₂×C₄×C₈	D₄₇
hypocenter	C₄₇	#1834
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂³

C₂×D₁₈₈

commutator

C₂×C₄×C₄₇

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₂×C₄×C₈×C₄₇

C₂

socle

C₂³×C₄₇

C₂×D₄

hypercenter

C₂×C₄×C₈

D₄₇

hypocenter

C₄₇

#1834

LCS

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

N	H ≅ G/N	type
9. C₄×C₈×C₄₇	C₄	semidirect
53. C₄₇	#1834	semidirect
59. C₄×C₈	Dic₄₇	semidirect

H ≅ G/N

type

9. C₄×C₈×C₄₇

C₄

semidirect

53. C₄₇

#1834

semidirect

59. C₄×C₈

Dic₄₇

semidirect

Subgroups — #20243516

Conjugacy classes of subgroups

Complements